Results 51 to 60 of about 793,110 (397)
Journal of Mathematical and Fundamental Sciences, 2018 A new method to treat the inherent instability of Lanczos-type algorithms is introduced. It enables us to capture the properties of the sequence of iterates generated by a Lanczos-type algorithm by interpolating on this sequence of points.
Maharani +2 more
doaj +1 more source
Resurgent extrapolation: rebuilding a function from asymptotic data. Painlevé I [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 Extrapolation is a generic problem in physics and mathematics: how to use asymptotic data in one parametric regime to learn about the behavior of a function in another parametric regime. For example: extending weak coupling expansions to strong coupling,
O. Costin, G. Dunne
semanticscholar +1 more source
Neurocomputing, 2006 We present a framework for efficient extrapolation of reduced rank approximations, graph kernels, and locally linear embeddings (LLE) to unseen data. We also present a principled method to combine many of these kernels and then extrapolate them. Central to our method is a theorem for matrix approximation, and an extension of the representer theorem to ...
Vishwanathan, S +3 more
openaire +4 more sources
Concept Extrapolation: A Conceptual Primer [PDF]
arXiv, 2023 This article is a primer on concept extrapolation - the ability to take a concept, a feature, or a goal that is defined in one context and extrapolate it safely to a more general context. Concept extrapolation aims to solve model splintering - a ubiquitous occurrence wherein the features or concepts shift as the world changes over time.
arxiv
Location Attention for Extrapolation to Longer Sequences [PDF]
Annual Meeting of the Association for Computational Linguistics, 2019 Neural networks are surprisingly good at interpolating and perform remarkably well when the training set examples resemble those in the test set. However, they are often unable to extrapolate patterns beyond the seen data, even when the abstractions ...
Yann Dubois +3 more
semanticscholar +1 more source
Biosimilars: Extrapolation for oncology
Critical Reviews in Oncology/Hematology, 2016 A biosimilar is a biologic that is highly similar to a licensed biologic (the reference product) in terms of purity, safety and efficacy. If the reference product is licensed to treat multiple therapeutic indications, extrapolation of indications, i.e., approval of a biosimilar for use in an indication held by the reference product but not directly ...
G. Curigliano +3 more
openaire +4 more sources
Journal of Symbolic Computation, 2009 AbstractConsider a power series f∈R[[z]], which is obtained by a precise mathematical construction. For instance, f might be the solution to some differential or functional initial value problem or the diagonal of the solution to a partial differential equation. In cases when no suitable method is available beforehand for determining the asymptotics of
openaire +2 more sources
Position Interpolation Improves ALiBi Extrapolation [PDF]
arXiv, 2023 Linear position interpolation helps pre-trained models using rotary position embeddings (RoPE) to extrapolate to longer sequence lengths. We propose using linear position interpolation to extend the extrapolation range of models using Attention with Linear Biases (ALiBi). We find position interpolation significantly improves extrapolation capability on
arxiv
Bayesian approach to model-based extrapolation of nuclear observables [PDF]
Physical Review C, 2018 The mass, or binding energy, is the basis property of the atomic nucleus. It determines its stability, and reaction and decay rates. Quantifying the nuclear binding is important for understanding the origin of elements in the universe.
L. Neufcourt +3 more
semanticscholar +1 more source
Extrapolation Frameworks in Cognitive Psychology Suitable for Study of Image Classification Models [PDF]
arXiv, 2021 We study the functional task of deep learning image classification models and show that image classification requires extrapolation capabilities. This suggests that new theories have to be developed for the understanding of deep learning as the current theory assumes models are solely interpolating, leaving many questions about them unanswered.
arxiv